Table Of ContentI.V.SAVELYEV
PHYSICS
A GENERAL COURSE
(Inthreevolumes)
VOLUME II
ELECTRICITY
AND MAGNETISM
WAVES
OPTICS
MIRPUBLISHERS
MOSCOW
TranslatedfromRussianbyG.Leib
Firstpublished1980
Revisedfromthe1978Russianedition
Secondprinting1985
Thirdprinting1989
PrintedintheUnionofSovietSocialistRepublics
ISBN5-03-000902-7,1978
ISBN5-03-000900-0,1980
v
PREFACE
Themaincontentofthepresentvolumeisthescienceofelectromagnetismandthe
scienceofwaves(elastic,electromagnetic,andlight).
The International System of Units (SI) has been used throughout the book,
although the reader is simultaneously acquainted with the Gaussian system. In
additiontoalistofsymbols,theappendicesattheendofthebookgivetheunitsof
electricalandmagneticquantitiesintheSIandintheGaussiansystemofunits,and
alsocomparetheformofthebasicformulasofelectromagnetisminbothsystems.
Thecourseistheresultoftwentyfiveyear’sworkintheDepartmentofGeneral
PhysicsoftheMoscowInstituteofEngineeringPhysics. Iamgratefultomycol-
leaguesandfriendsfortheirhelpfuldiscussions,criticismandadviceinthecourse
ofthepreparationofthebook.
Thepresentcourseisintendedaboveallforhighertechnicalschoolswithan
extendedsyllabusinphysics.Thematerialhasbeenarranged,however,sothatthe
bookcanbeusedasateachingaidforhighertechnicalschoolswithanordinary
syllabussimplybyomittingsomesections.
IgorSavelyev
Moscow,November,1979
CONTENTS vii
Contents
Preface v
I ELECTRICITYANDMAGNETISM 1
Chapter1. ELECTRICFIELDINAVACUUM 3
1.1 ElectricCharge 3
1.2 Coulomb’sLaw 4
1.3 SystemsofUnits 7
1.4 RationalizedFormofWritingFormulas 8
1.5 ElectricField.FieldStrength 9
1.6 Potential 12
1.7 InteractionEnergyofaSystemofCharges 16
1.8 RelationBetweenElectricFieldStrengthandPotential 17
1.9 Dipole 20
1.10 FieldofaSystemofChargesatGreatDistances 25
1.11 ADescriptionofthePropertiesofVectorFields 28
1.12 CirculationandCurlofanElectrostaticField 43
1.13 Gauss’sTheorem 45
1.14 CalculatingFieldswiththeAidofGauss’sTheorem 47
Chapter2. ELECTRICFIELDINDIELECTRICS 53
2.1 PolarandNon-PolarMolecules 53
2.2 PolarizationofDielectrics 55
2.3 TheFieldInsideaDielectric 56
2.4 SpaceandSurfaceBoundCharges 57
2.5 ElectricDisplacementVector 62
2.6 ExamplesofCalculatingtheFieldinDielectrics 65
2.7 ConditionsontheInterfaceBetweenTwoDielectrics 69
2.8 ForcesActingonaChargeinaDielectric 72
2.9 Ferroelectrics 74
Chapter3. CONDUCTORSINANELECTRICFIELD 77
3.1 EquilibriumofChargesonaConductor 77
3.2 AConductorinanExternalElectricField 80
viii CONTENTS
3.3 Capacitance 80
3.4 Capacitors 82
Chapter4. ENERGYOFANELECTRICFIELD 85
4.1 EnergyofaChargedConductor 85
4.2 EnergyofaChargedCapacitor 85
4.3 EnergyofanElectricField 88
Chapter5. STEADYELECTRICCURRENT 93
5.1 ElectricCurrent 93
5.2 ContinuityEquation 96
5.3 ElectromotiveForce 97
5.4 Ohm’sLaw.ResistanceofConductors 99
5.5 Ohm’sLawforanInhomogeneousCircuitSection 101
5.6 MultiloopCircuits.Kirchhoff’sRules 103
5.7 PowerofaCurrent 106
5.8 TheJoule-LenzLaw 107
Chapter6. MAGNETICFIELDINAVACUUM 109
6.1 InteractionofCurrents 109
6.2 MagneticField 112
6.3 FieldofaMovingCharge 113
6.4 TheBiot-SavartLaw 116
6.5 TheLorentzForce 119
6.6 Ampere’sLaw 122
6.7 MagnetismasaRelativisticEffect 124
6.8 CurrentLoopinaMagneticField 130
6.9 MagneticFieldofaCurrentLoop 135
6.10 WorkDoneWhenaCurrentMovesinaMagneticField 138
6.11 DivergenceandCurlofaMagneticField 142
6.12 FieldofaSolenoidandToroid 146
Chapter7. MAGNETICFIELDINASUBSTANCE 151
7.1 MagnetizationofaMagnetic 151
7.2 MagneticFieldStrength 152
7.3 CalculationoftheFieldinMagnetics 158
7.4 ConditionsattheInterfaceofTwoMagnetics 160
7.5 KindsofMagnetics 164
7.6 GyromagneticPhenomena 164
7.7 Diamagnetism 169
7.8 Paramagnetism 173
7.9 Ferromagnetism 175
Chapter8. ELECTROMAGNETICINDUCTION 181
8.1 ThePhenomenonofElectromagneticInduction 181
8.2 InducedE.M.F. 182
8.3 WaysofMeasuringtheMagneticInduction 186
8.4 EddyCurrents 187
8.5 Self-Induction 189
CONTENTS ix
8.6 CurrentWhenaCircuitIsOpenedorClosed 191
8.7 MutualInduction 194
8.8 EnergyofaMagneticField 196
8.9 WorkinMagneticReversalofaFerromagnetic 198
Chapter9. MAXWELL’SEQUATIONS 201
9.1 VortexElectricField 201
9.2 DisplacementCurrent 203
9.3 Maxwell’sEquations 207
Chapter10. MOTIONOFCHARGEDPARTICLESINELECTRIC
ANDMAGNETICFIELDS 211
10.1 MotionofaChargedParticleinaHomogeneousMagneticField 211
10.2 DeflectionofMovingChargedParticlesbyanElectricandaMagneticField 213
10.3 DeterminationoftheChargeandMassofanElectron 216
10.4 DeterminationoftheSpecificChargeofIons.MassSpectrographs 221
10.5 ChargedParticleAccelerators 225
Chapter11. THECLASSICALTHEORYOFELECTRICALCONDUCTANCE
OFMETALS 231
11.1 TheNatureofCurrentCarriersinMetals 231
11.2 TheElementaryClassicalTheoryofMetals 233
11.3 TheHallEffect 237
Chapter12. ELECTRICCURRENTINGASES 241
12.1 Semi-Self-SustainedandSelf-SustainedConduction 241
12.2 Semi-Self-SustainedGasDischarge 241
12.3 IonizationChambersandCounters 245
12.4 ProcessesLeadingtotheAppearanceofCurrentCarriers 250
12.5 Gas-DischargePlasma 254
12.6 GlowDischarge 256
12.7 ArcDischarge 259
12.8 SparkandCoronaDischarges 260
Chapter13. ELECTRICALOSCILLATIONS 265
13.1 QuasistationaryCurrents 265
13.2 FreeOscillationsinaCircuitWithoutaResistance 266
13.3 FreeDampedOscillations 269
13.4 ForcedElectricalOscillations 273
13.5 AlternatingCurrent 277
II WAVES 281
Chapter14.ELASTICWAVES 283
14.1 PropagationofWavesinanElasticMedium 283
14.2 EquationsofaPlaneandaSphericalWave 286
14.3 EquationofaPlaneWavePropagatinginanArbitraryDirection 289
x CONTENTS
14.4 TheWaveEquation 291
14.5 VelocityofElasticWavesinaSolidMedium 292
14.6 EnergyofanElasticWave 294
14.7 StandingWaves 299
14.8 OscillationsofaString 302
14.9 Sound 303
14.10 TheVelocityofSoundinGases 306
14.11 TheDopplerEffectforSoundWaves 311
Chapter15. ELECTROMAGNETICWAVES 313
15.1 TheWaveEquationforanElectromagneticField 313
15.2 PlaneElectromagneticWave 315
15.3 ExperimentalInvestigationofElectromagneticWaves 318
15.4 EnergyofElectromagneticWaves 319
15.5 MomentumofElectromagneticField 322
15.6 DipoleEmission 324
III OPTICS 329
Chapter16. OPTICS 331
16.1 TheLightWave 331
16.2 RepresentationofHarmonicFunctionsUsingExponents 334
16.3 ReflectionandRefractionofaPlaneWaveattheInterfaceBetweenTwo
Dielectrics 336
16.4 LuminousFlux 342
16.5 PhotometricQuantitiesandUnits 343
16.6 GeometricalOptics 347
16.7 CenteredOpticalSystem 351
16.8 ThinLenses 358
16.9 Huygens’Principle 359
Chapter17. INTERFERENCEOFLIGHT 361
17.1 InterferenceofLightWaves 361
17.2 Coherence 366
17.3 WaysofObservingtheInterferenceofLight 374
17.4 InterferenceofLightReflectedfromThinPlates 376
17.5 TheMichelsonInterferometer 386
17.6 MultibeamInterference 389
Chapter18. DIFFRACTIONOFLIGHT 397
18.1 Introduction 397
18.2 Huygens-FresnelPrinciple 398
18.3 FresnelZones 401
18.4 FresnelDiffractionfromSimpleBarriers 406
18.5 FraunhoferDiffractionfromaSlit 417
18.6 DiffractionGrating 425
18.7 DiffractionofX-Rays 434
